Year: 2018
Author: D. J. Liu, A. Q. Li, Z. R. Chen
Advances in Applied Mathematics and Mechanics, Vol. 10 (2018), Iss. 6 : pp. 1365–1383
Abstract
The $p$-Laplace problems in topology optimization eventually lead to a degenerate convex minimization problem $E(v):= ∫_ΩW(∇v)dx − ∫_Ωf vdx$ for $v∈W^{1,p}_0(Ω)$ with unique minimizer $u$ and stress $σ := DW(∇u)$. This paper proposes the discrete Raviart-Thomas mixed finite element method (dRT-MFEM) and establishes its equivalence with the Crouzeix-Raviart nonconforming finite element method (CR-NCFEM). The sharper quasi-norm a priori and a posteriori error estimates of this two methods are presented. Numerical experiments are provided to verify the analysis.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aamm.OA-2018-0117
Advances in Applied Mathematics and Mechanics, Vol. 10 (2018), Iss. 6 : pp. 1365–1383
Published online: 2018-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 19
Keywords: Adaptive finite element methods nonconforming $p$-Laplace problem dual energy.